Re: integer cube root ...

Gerard Schildberger <Gerard46@xxxxxxx> wrote:

What I'm looking for is a specific routine just for integer cube roots,
similar to the integer square root (above), which isn't (as far as I
know, an integer version of Newton's method). I know there is one, and
I was hoping that somebody whould know of it (or where it is on the www).
The general routine (above) for any root seems like overkill for what I
wanted to do. __________________________________________________Gerard S.


Find a book an how to use an abacus that includes square
and cube roots. I once bought a cheap abacus in a chinatown
store that included a little book.

For the square root algorithm, similar to the integer square
root algorithm you mention, successive odd integers are subtracted
from the high digit, and the number of such is counted.
(The sum of the first n odd integers is n**2.)
(Though with a shift of the decimal point it will work for
fixed point non-integer numbers, too.)

Then there is a correction when you shift to the next lower digits
(one in the accumulating square root, and two in the ever decreasing
starting number.) The square root algorithm comes from the identity
(10A+B)**2=100A+20AB+B**2

The cube root algorithm takes three sets of abacus columns,
accumulating x and x**2 while reducing the original number by x**3.
(For more digits you put two abaci side by side.)

See: http://hem.passagen.se/ceem/china.htm

The cube root algorithm comes from:
(10A+B)**3=1000A**3+300*A**2*B+30*A*B**2+B**3


-- glen
.

Relevant Pages

  • Re: Points on elliptic curves
    ... also a homomorphism of additive groups. ... What does this have to do with quadratic equations? ... a double root and exists, because all the elements of GFhave a unique square root. ... a "trace condition" splits the quadratic equation into two cases more or less equiprobable cases just like the study of the square root of the discriminant does in the case of characteristic not equal to two. ...
    (sci.math)
  • Re: Marie Jean Faucounau sues me for at least 8,487 Swiss Fr
    ... Your are just talking about the SQUARE ROOT columns, ... I'M ASKING YOU SPECIFICALLY ABOUT THE CUBE ROOT COLUMN: ... mistake is diminishing. ...
    (sci.lang)
  • Re: cube root of a given number
    ... the Householder expressions for the Nth root of any number P. ... Higher-order rational process based on the Rational Mean: ... approximations -by defect and excess-- to the square root of P. ... multiply by THREE the number of exact digits in each iteration. ...
    (sci.math)
  • Re: integer cube root ...
    ... |> What I'm looking for is a specific routine just for integer cube roots, ... |> The general routine for any root seems like overkill for what I ... | root algorithm you mention, ... | (one in the accumulating square root, and two in the ever decreasing ...
    (comp.lang.pl1)
  • Re: Fixed Point Square Root Improvements?
    ... > able to find the square root of a 16.16 fixed point integer. ... one Marine noticed one of the prisoners was still breathing. ... He faking he's fucking dead." ...
    (comp.lang.asm.x86)